Lat. ad quietem arg.; quies, “rest; in politics, peaceful period; neutrality”.

Calm is the emotional and cognitive state of a person having no reason for concern, in particular, having no urgent issue to address.
Serious argumentative situations are inherently tense. The involved participants themselves may wish to wish to get out of it as soon as possible, in order to restore their former, real or imagined tranquility. But it would be best not to have to debate: the burden of proof is the price paid by the proponent for disturbing the tranquility of the group. 

1. Calm and emotionality

The Aristotelian list of socio-rhetorical emotions opposes calm to anger, S. Emotion. In fact, calm may be opposed to any strong positive or negative emotion. Strong emotions are characterized by a marked variation of arousal. Specific actions, speech and arguments might be used to reduce such excitation and re-instill a quieter mood, that is to calm down overexcited people, be they a group of enthusiasts enraged by the prospect of a war, or children throwing a tantrum.

2. Appeal to tranquility

In the political sphere, the ad quietem maneuver has been identified and labelled ad quietem by Bentham (1824; S. Political Arguments). It is defined as an attempt to postpone the discussion of a proposal in the hope that the issue will never be addressed.
iscourses amplifying the following topics are central to this move:

This issue is not so important, already settled, we have other priorities, we’ll discuss that later, you are the only one to see that as a problem…
Leave us alone with these things!

A meta-discussion about the relevance and timing of the discussion is substituted for the discussion itself. Bentham regards this maneuver as fallacious, and classifies it in the category of “fallacies of delay”, directed against freedom of proposition and political innovation.

The appeal to tranquility values calm as a peaceful conservative social state, which may side with apathy, inertia and laziness. Dissatisfied proponents, ready to argue for innovations and changes, speaking possibly in the best common interest, are framed as troublemakers, instilling adrenaline, excitation, anger and anxiety within the group.

Tranquility may be invoked as an argument for not participating in political and social life:

Voting concerns only men, since women — fortunately for their tranquility — do not have political rights.
Clarisse Juranville, [Handbook of Moral Education and Civic Instruction], [1911].[1]

The following interventions are taken from a debate on immigration and French nationality, a quite topical issue at that time. At the very beginning of the discussion A, a female student,  first alludes to the handouts that were distributed to students, then, she  gives a carefully worded and slightly oriented description of the two parties and of their positions. Finally, on the basis of a perfect “leave us in peace” argumentation, she takes an implicit but clear stand in favor of the party holding that “the government currently has other priorities that are more important and that it [is] not necessary to go back to this point”:

 Prof:       then you say nothing stay mute/ you learned nothing from all that, nothing struck you/ — you what are the points/ — so let’s start listing them\ you can give them/ yes/
A:             already two points of view actually, finally
Prof:        there are two points of view you have seen that there was yes/
A:             two parties that oppose well those who want to— as the petition of all the screen actors and filmmakers etcetera who want that: im- well the nationality code be unlimited\ and that all the— undocumented people be regularized\ therefore hmm without any limit
Prof:        hm hm hm hm (1)
A:            and the second point of view is those who say that for there to be a right of the people there must be:: a right of state\ therefore precisely there must be limits and that:: and also these people are those who say that the government currently has other priorities that are more important and that it was not necessary to go back to that point\
Prof:        OK (1)

(1) ratifies the previous turn, without taking a stand.
Corpus On Immigration and French Nationality, Student Workshop.[2]

[1] Quoted after Clarisse Juranville, Manuel d’éducation morale et d’instruction civique civique [Manual of moral education and civic instruction], Paris: Vve P. Larousse.
Quoted after the 5e ed., 1re part Éducation morale [Moral Education]; chap. Le vote [The Vote]; § Les femmes et la politique [Women and Politics]. No Date. No pag.

[2] Corpus Débats sur l’immigration — Débat étudiants [Debates on immigration — Students]. CLAPI data base, Num_corpus = 35] (07-30-2013).